Compare equal quantities, not unequal orders
A three-unit order can generate more contribution than a one-unit order while earning less per item. That alone does not justify a volume discount. This tool compares one bulk order with the same number of units sold in separate, full-price orders, so a quantity change does not disguise the discount's cost.
Use the total shipping cost for the bulk order, not a per-item amount. The single-order shipping and fixed fee are charged once for every unit in the separate-sales scenario. For the bulk scenario, the fixed fee is charged once. Item acquisition cost is still multiplied by quantity in both cases.
How the calculation works
Let q be quantity, P regular unit price, d the discount divided by 100, c unit cost, r combined percentage charges divided by 100 and F the fixed order fee.
Bulk contribution = q × P × (1 − d) × (1 − r) − q × c − bulk shipping − F
Separate contribution = q × [P × (1 − r) − c − single shipping − F]
Break-even bulk unit price = (q × c + bulk shipping + F) ÷ [q × (1 − r)]
Zero-contribution discount limit (%) = (1 − break-even unit price ÷ P) × 100
Break-even calculations require percentage charges below 100%. A regular price of zero makes the discount-limit percentage undefined. A negative limit means the full regular price is already below break-even; it is not a discount opportunity.
Worked example: a 15% discount on three units
Start with a $30 unit price, $12 unit cost and a quantity of three. Apply a 15% discount and 5% fee. Shipping costs $5 for each separate order or $7 for the bulk order, with no fixed order fee.
| Measure | Arithmetic | Result |
|---|---|---|
| Discounted price | $30 × 0.85 | $25.50/unit |
| Bulk contribution | $76.50 × 0.95 − $36 − $7 | $29.675 → $29.68 |
| Separate contribution | 3 × ($30 × 0.95 − $12 − $5) | $34.50 |
| Bulk minus separate | $29.675 − $34.50 | −$4.825 → −$4.83 |
Results are computed at full precision before display, so subtracting two displayed amounts can differ by a cent from the displayed difference. Bulk contribution margin is about 38.79%. The zero-contribution unit price is $43 ÷ 2.85 = $15.0877… and the corresponding discount limit is about 49.71%.
Break-even is different from preserving earnings
The 49.71% threshold covers only entered costs. To preserve the $34.50 contribution from separate sales, bulk revenue must cover $43 of cost plus $34.50 of contribution. Dividing $77.50 by 0.95 gives $81.5789… total revenue, or $27.193… per unit. That corresponds to about a 9.36% discount before cent rounding. The 15% example gives away more revenue than shipping savings recover.
This comparison assumes every unit would otherwise sell at full price in its own order. If the real alternative is one customer buying several units without a discount, separate-order savings may not exist. Model that baseline separately before adopting a promotion. Demand, conversion, repeat purchase behavior and inventory constraints are not predicted.